On the finite-time blow-up of the solution of the Cauchy problem for the pseudoparabolic equation Aut=F(u)статья
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Аннотация:We study the abstract Cauchy problem for a differential equation with operator coefficients in a Banach space. For any initial values of the solution of the Cauchy problem in a certain Banach space V^, under certain assumptions on the operator coefficients we prove the finite-time blow-up of the solution. In the classes considered we obtain lower and upper bounds on the time of blow-up and lower and upper bounds on the rate of blow-up of the solution of the problem considered. We give examples of operators that satisfy the conditions introduced in the paper